Positive definite matrix, conditionally negative definite matrix, infinitely divisible matrix, Hadamard inverse, means.
In earlier papers R. Bhatia and H. Kosaki have shown that certain matrices associated with means are infinitely divisible. In this paper it is shown that many of them possess a stronger property: their Hadamard reciprocals have exactly one positive eigenvalue.
Bhatia, Rajendra and Jain, Tanvi.
"Mean matrices and conditional negativity",
Electronic Journal of Linear Algebra,
Volume 29, pp. 206-222.